# Free Resource: Strength of Materials made Easy

If you haven’t been able to tell yet, I LOVE finding and creating shortcuts to everyday problems. Any time I find myself doing repetitive work I can’t help but think about different ways to automate the task. It’s just a good habit to make anyway because we all have that sort of work to do sometimes and thinking this way can make mundane tasks a bit more enjoyable to grind though.

As a mechanical engineer, one such task I commonly encounter is calculating the stress in simple beams. Any experienced designer can usually just look at a beam and determine if it is strong enough for its intended purpose, but that’s a really foolish way to design important parts. Actual engineering math needs to be performed to justify your selection of material and size for any critical machine components.

Unfortunately, it takes a fair amount of time to setup and run stress analysis simulations on a computer (and that’s only an option if you have access to the software1). So I have often found myself cracking open a stress analysis textbook and punching numbers into my TI-30XII (ol’ reliable), which leaves me staring down a fairly mundane task every time I tweak the design.

Did you say ‘actual engineering math’…

And so I created a basic strength of materials calculator to reduce the time spent calculating the same thing over and over. Of course, like many other things I create here, it is an Excel document because that program is ubiquitous and so darn awesome anyway.

The calculator uses a few user-inputs to determine the mechanical properties of beams of various materials and cross sections including round, square, tube, angle, and I-beam. You can use it to quickly estimate a given beam’s weight, ultimate tensile strength, and shear strength among other things. It also includes buckling load and cantilever beam calculations. It’s not even a very big worksheet but it really is all you need for the majority of diy projects and simple machines. So go ahead and check it out here, I’ll wait.

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Now as great as this little calculator is, it is in no way a replacement for having taken an actual strength of materials class. While I have found that many of the courses I took in college are utterly useless to my career, strength of materials is not among them. It is in classes like this one that you learn certain subtleties that you might miss out on if you are self taught. I thought it would be fun to talk a bit about one of those.2

Perhaps you have found yourself wondering what are the advantages and disadvantages of different beam cross sections? What shape makes the most efficient use of material weight to create a stiff structural member? When constrained by weight, is it better to make beams thicker or have larger outer dimensions?

It turns out that the answers to these questions, like everything else in engineering, depends on your application. Different cross sections have different strengths and weaknesses and you have to balance tradeoffs to match the application. I created this handy dandy chart to make the selection process a little easier.

It may have been more correct to say stronger or weaker because the chart is just intended to compare the relative strengths of the different shapes. To be clear, wide but thin beams are great at resisting twisting forces and bending/buckling loads, but it comes at a cost of transverse shear resistance and increased risk of the tube walls caving in while being crushed from the side (dented).

Thick walled but smaller outer diameter tubes are the exact opposite.  Similarly, circles are more efficient at resisting torsion and shear than squares, but not bending. Polygon shapes are somewhere in the middle. And triangles…have you ever seen a beam with a triangular cross section?

Admittedly, comparing tubes to open cross sections is a bit like comparing apples to oranges, but for general design purposes the above chart will be useful. Open sections are generally best used to resist unidirectional bending loads. If buckling is a concern then you need to support open sections on their weak axis.

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1. Unfortunately, I have yet to find any free stress analysis software available on the internet, please let me know if you do!
2. I know… some of the things I think are fun are kind of weird.

1. […] specimen.  Unfortunately, its strength was limited to the tensile strength of four 5/16” bolts (roughly 27,261 lbs thank you). Also this device was difficult to keep centered on the test machine, it couldn’t be used on […]

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2. This is awesome. I kinda wish that I did engineering as my uni degree (instead of I.T which I am studying now) as in my spare time I hang out with the local robosoc and build things haha.

Any change of adding 3d printable materials to the spreadsheet? (PLA,ABS etc) I know they are not even on the same level (and they vary depending on pigment), but I’m sure that would be of use to some makers too.

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• Great idea, I’ll do that when I get the chance! Of course you know that 3d printed parts have directional strength because of the way they are manufactured, but it would still be useful as an estimate.
You might also be interested to know that I have longer term plans to run some mechanical tests on 3D printed objects to determine the effect of infill % and pattern. I wonder how the results will stack up against the estimates from the strength of materials worksheet?

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• Awesome :DD I don’t think any of that has been done before, so assuming the calculations and terminology aren’t too hard it has the potential to be very useful!

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3. Hey I updated the strength of materials worksheet (though you can’t tell because I haven’t instituted any sort of a revision log yet).

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4. You can certainly see your expertise within the article you write.

The world hopes for even more passionate writers such as you who are not afraid to say how they believe.

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5. xuan tran says:

Great website. I’m using this spreadsheet to help a HS robotics team determine which shape (profile) to use for a component that will experience bending.

I was showing them the difference between a rectangular, hollow tube vs a round one of similar size and identical length, constraint, and load, but when I used the CAE tool on my CAD system to calculate the same deflection… I got a higher deflection value (i.e. Spreadsheet = 0.013″ vs CAE = 0.4″. Material is 6160 Al.

The only difference I saw was that the CAE had the following:
YS = 35,000 (spreadsheet = 27,500)
US = 40,000 (spreadsheet = 30,938)

Is that difference enough to result in such a large disparity?